Two-Stage Robust Sizing and Operation Co-Optimization for Residential PV-Battery Systems Considering the Uncertainty of PV Generation and Load

This article presents a two-stage adaptive robust optimization (ARO) for optimal sizing and operation of residential solar photovoltaic (PV) systems coupled with battery units. Uncertainties of PV generation and load are modeled by user-defined bounded intervals through polyhedral uncertainty sets. The proposed model determines the optimal size of PV-battery system while minimizing operating costs under the worst-case realization of uncertainties. The ARO model is proposed as a trilevel min-max-min optimization problem. The outer min problem characterizes sizing variables as 'here-and-now' decisions to be obtained prior to uncertainty realization. The inner max-min problem, however, determines the operation variables in place of 'wait-and-see' decisions to be obtained after uncertainty realization. An iterative decomposition methodology is developed by means of the column-and-constraint technique to recast the trilevel problem into a single-level master problem (the outer min problem) and a bilevel subproblem (the inner max-min problem). The duality theory and the Big-M linearization technique are used to transform the bilevel subproblem into a solvable single-level max problem. The immunization of the model against uncertainties is justified by testing the obtained solutions against 36 500 trial uncertainty scenarios in a postevent analysis. The proposed postevent analysis also determines the optimum robustness level of the ARO model to avoid over/under conservative solutions.